46. If a man receives on one-fourth of his capital 3% interest, on two third 5% and on the remainder 11%, the percentage he receives on the whole is
    

1. 1. 4.5%
      

   
   
   

   2. 5%
      

   
   
   

   3. 5.5%
      

   
   
   

   4. 5.2%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   According to question , we have
   

   Required percent =	1	× 3 +	2	× 5 +		1 -	1	-	2		× 11
   	4		3				4		3

   
   

   Correct Option: B

   According to question , we have
   

   Required percent =	1	× 3 +	2	× 5 +		1 -	1	-	2		× 11
   	4		3				4		3

   
   

   Required percent =	3	+	10	+	11	=	9 + 40 + 11	= 5%
   	4		3		12		12

---

47. Arun lends ₹ 20,000 to two of his friends. He gives ₹ 12,000 to the first at 8% p.a. simple interest. Arun wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is
    

1. 1. 8%
      

   
   
   

   2. 16%
      

   
   
   

   3. 12%
      

   
   
   

   4. 13%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   We know that ,
   

   ∴ SI =	P × R × T
   	100

   
   According to question ,
   

   S.I. on 12000 =	12000 × 8 × 1	= ₹ 960
   	100

   
   Desired gain on ₹ 20000
   = 20000 × (10 ÷ 100) = ₹ 2000
   ∴ S.I. on ₹ 8000 = 2000 – 960 = ₹ 1040
   

   Correct Option: D

   We know that ,
   

   ∴ SI =	P × R × T
   	100

   
   According to question ,
   

   S.I. on 12000 =	12000 × 8 × 1	= ₹ 960
   	100

   
   Desired gain on ₹ 20000
   = 20000 × (10 ÷ 100) = ₹ 2000
   ∴ S.I. on ₹ 8000 = 2000 – 960 = ₹ 1040
   

   ∴ Rate =	SI × 100
   	Principal × Time

   
   

   Rate =	1040 × 100
   	800

   
   Rate = 13% per annum

---

---

48. A person lends 40% of his sum of money at 15% per annum, 50% of rest at 10% per annum and the rest at 18% per annum rate of interest. What would be the annual rate of interest, if the interest is calculated on the whole sum ?
    

1. 1. 13.4%
      

   
   
   

   2. 14.33%
      

   
   
   

   3. 14.4%
      

   
   
   

   4. 13.33%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the person have ₹ 100.
   Then
   

   SI for 1 year = ₹		40 × 15 × 1	+	30 × 10 × 1	+	30 × 18 × 1
   		100		100		100

   
   

   Correct Option: C

   Let the person have ₹ 100.
   Then
   

   SI for 1 year = ₹		40 × 15 × 1	+	30 × 10 × 1	+	30 × 18 × 1
   		100		100		100

   
   SI for 1 year = ₹ (6 + 3 + 5.4) = ₹ 14.4
   ∴ Rate of interest on whole sum = 14.4%

---

49. The effective annual rate of interest, corresponding to a nominal rate of 6% per annum payable half yearly, is :
    

1. 1. 6.06%
      

   
   
   

   2. 6.07%
      

   
   
   

   3. 6.08%
      

   
   
   

   4. 6.09%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the sum be ₹ 100.
   For initial six months,
   

   Simple Interest = 100 ×	6	×	6	= 3%
   	100		12

   
   Now, sum = 100 + 3 = ₹ 103
   For another six months,
   

   Correct Option: D

   Let the sum be ₹ 100.
   For initial six months,
   

   Simple Interest = 100 ×	6	×	6	= 3%
   	100		12

   
   Now, sum = 100 + 3 = ₹ 103
   For another six months,
   

   Simple Interest = 103 ×	6	×	6	= 3.09
   	100		12

   
   ∴ Rate of interest per annum = 3 + 3.09 = 6.09%

---

---

50. A sum of ₹ 1000 is lent out partly at 8% and the remaining at 10% per annum. If the yearly income on the average is 9.2%, the two parts respectively are
    

1. 1. ₹ 400, ₹ 600
      

   
   
   

   2. ₹450, ₹ 550
      

   
   
   

   3. ₹ 500, ₹ 500
      

   
   
   

   4. ₹ 550, ₹ 450

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let p be lent on 8%.
   ∴ (1000 – p ) is lent on 10%.
   Simple Interest = 9.2% of 1000 = ₹ 92
   

   SI =	P × R × T
   	100

   
   

   ∴ 92 =	p × 8	+		(1000 - p)		× 10
   	100			100

   
   

   Correct Option: A

   Let p be lent on 8%.
   ∴ (1000 – p ) is lent on 10%.
   Simple Interest = 9.2% of 1000 = ₹ 92
   

   SI =	P × R × T
   	100

   
   

   ∴ 92 =	p × 8	+		(1000 - p)		× 10
   	100			100

   
   ⇒ 8p + 10000 – 10p = 9200
   ⇒ – 2p = 9200 – 10000
   ⇒ p = 800 ÷ 2 = ₹ 400 = First part
   ∴ Second part = ₹ 600

---